Properties

Label 300.2.i.a.293.1
Level $300$
Weight $2$
Character 300.293
Analytic conductor $2.396$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 293.1
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 300.293
Dual form 300.2.i.a.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61803 + 0.618034i) q^{3} +(1.00000 - 1.00000i) q^{7} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+(-1.61803 + 0.618034i) q^{3} +(1.00000 - 1.00000i) q^{7} +(2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(3.00000 + 3.00000i) q^{13} +(2.23607 + 2.23607i) q^{17} +2.00000i q^{19} +(-1.00000 + 2.23607i) q^{21} +(-2.23607 + 2.23607i) q^{23} +(-2.38197 + 4.61803i) q^{27} +4.47214 q^{29} +4.00000 q^{31} +(-2.76393 - 7.23607i) q^{33} +(3.00000 - 3.00000i) q^{37} +(-6.70820 - 3.00000i) q^{39} -8.94427i q^{41} +(3.00000 + 3.00000i) q^{43} +(-6.70820 - 6.70820i) q^{47} +5.00000i q^{49} +(-5.00000 - 2.23607i) q^{51} +(2.23607 - 2.23607i) q^{53} +(-1.23607 - 3.23607i) q^{57} -8.94427 q^{59} -6.00000 q^{61} +(0.236068 - 4.23607i) q^{63} +(1.00000 - 1.00000i) q^{67} +(2.23607 - 5.00000i) q^{69} -4.47214i q^{71} +(-1.00000 - 1.00000i) q^{73} +(4.47214 + 4.47214i) q^{77} +6.00000i q^{79} +(1.00000 - 8.94427i) q^{81} +(6.70820 - 6.70820i) q^{83} +(-7.23607 + 2.76393i) q^{87} -4.47214 q^{89} +6.00000 q^{91} +(-6.47214 + 2.47214i) q^{93} +(-9.00000 + 9.00000i) q^{97} +(8.94427 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 4q - 2q^{3} + 4q^{7} + 12q^{13} - 4q^{21} - 14q^{27} + 16q^{31} - 20q^{33} + 12q^{37} + 12q^{43} - 20q^{51} + 4q^{57} - 24q^{61} - 8q^{63} + 4q^{67} - 4q^{73} + 4q^{81} - 20q^{87} + 24q^{91} - 8q^{93} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.61803 + 0.618034i −0.934172 + 0.356822i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 1.00000i 0.377964 0.377964i −0.492403 0.870367i \(-0.663881\pi\)
0.870367 + 0.492403i \(0.163881\pi\)
\(8\) 0 0
\(9\) 2.23607 2.00000i 0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0 0
\(13\) 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i \(-0.0497784\pi\)
−0.155747 + 0.987797i \(0.549778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.23607 + 2.23607i 0.542326 + 0.542326i 0.924210 0.381884i \(-0.124725\pi\)
−0.381884 + 0.924210i \(0.624725\pi\)
\(18\) 0 0
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) 0 0
\(21\) −1.00000 + 2.23607i −0.218218 + 0.487950i
\(22\) 0 0
\(23\) −2.23607 + 2.23607i −0.466252 + 0.466252i −0.900698 0.434446i \(-0.856944\pi\)
0.434446 + 0.900698i \(0.356944\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.38197 + 4.61803i −0.458410 + 0.888741i
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) −2.76393 7.23607i −0.481139 1.25964i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 0 0
\(39\) −6.70820 3.00000i −1.07417 0.480384i
\(40\) 0 0
\(41\) 8.94427i 1.39686i −0.715678 0.698430i \(-0.753882\pi\)
0.715678 0.698430i \(-0.246118\pi\)
\(42\) 0 0
\(43\) 3.00000 + 3.00000i 0.457496 + 0.457496i 0.897833 0.440337i \(-0.145141\pi\)
−0.440337 + 0.897833i \(0.645141\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.70820 6.70820i −0.978492 0.978492i 0.0212814 0.999774i \(-0.493225\pi\)
−0.999774 + 0.0212814i \(0.993225\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −5.00000 2.23607i −0.700140 0.313112i
\(52\) 0 0
\(53\) 2.23607 2.23607i 0.307148 0.307148i −0.536655 0.843802i \(-0.680312\pi\)
0.843802 + 0.536655i \(0.180312\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.23607 3.23607i −0.163721 0.428628i
\(58\) 0 0
\(59\) −8.94427 −1.16445 −0.582223 0.813029i \(-0.697817\pi\)
−0.582223 + 0.813029i \(0.697817\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0.236068 4.23607i 0.0297418 0.533694i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.00000i 0.122169 0.122169i −0.643379 0.765548i \(-0.722468\pi\)
0.765548 + 0.643379i \(0.222468\pi\)
\(68\) 0 0
\(69\) 2.23607 5.00000i 0.269191 0.601929i
\(70\) 0 0
\(71\) 4.47214i 0.530745i −0.964146 0.265372i \(-0.914505\pi\)
0.964146 0.265372i \(-0.0854949\pi\)
\(72\) 0 0
\(73\) −1.00000 1.00000i −0.117041 0.117041i 0.646160 0.763202i \(-0.276374\pi\)
−0.763202 + 0.646160i \(0.776374\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.47214 + 4.47214i 0.509647 + 0.509647i
\(78\) 0 0
\(79\) 6.00000i 0.675053i 0.941316 + 0.337526i \(0.109590\pi\)
−0.941316 + 0.337526i \(0.890410\pi\)
\(80\) 0 0
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 0 0
\(83\) 6.70820 6.70820i 0.736321 0.736321i −0.235543 0.971864i \(-0.575687\pi\)
0.971864 + 0.235543i \(0.0756868\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.23607 + 2.76393i −0.775788 + 0.296325i
\(88\) 0 0
\(89\) −4.47214 −0.474045 −0.237023 0.971504i \(-0.576172\pi\)
−0.237023 + 0.971504i \(0.576172\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) −6.47214 + 2.47214i −0.671129 + 0.256349i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.00000 + 9.00000i −0.913812 + 0.913812i −0.996570 0.0827581i \(-0.973627\pi\)
0.0827581 + 0.996570i \(0.473627\pi\)
\(98\) 0 0
\(99\) 8.94427 + 10.0000i 0.898933 + 1.00504i
\(100\) 0 0
\(101\) 8.94427i 0.889988i 0.895533 + 0.444994i \(0.146794\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) −1.00000 1.00000i −0.0985329 0.0985329i 0.656122 0.754655i \(-0.272196\pi\)
−0.754655 + 0.656122i \(0.772196\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.23607 + 2.23607i 0.216169 + 0.216169i 0.806882 0.590713i \(-0.201153\pi\)
−0.590713 + 0.806882i \(0.701153\pi\)
\(108\) 0 0
\(109\) 8.00000i 0.766261i −0.923694 0.383131i \(-0.874846\pi\)
0.923694 0.383131i \(-0.125154\pi\)
\(110\) 0 0
\(111\) −3.00000 + 6.70820i −0.284747 + 0.636715i
\(112\) 0 0
\(113\) 2.23607 2.23607i 0.210352 0.210352i −0.594065 0.804417i \(-0.702478\pi\)
0.804417 + 0.594065i \(0.202478\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 12.7082 + 0.708204i 1.17487 + 0.0654735i
\(118\) 0 0
\(119\) 4.47214 0.409960
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 0 0
\(123\) 5.52786 + 14.4721i 0.498431 + 1.30491i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 13.0000 13.0000i 1.15356 1.15356i 0.167731 0.985833i \(-0.446356\pi\)
0.985833 0.167731i \(-0.0536439\pi\)
\(128\) 0 0
\(129\) −6.70820 3.00000i −0.590624 0.264135i
\(130\) 0 0
\(131\) 4.47214i 0.390732i 0.980730 + 0.195366i \(0.0625895\pi\)
−0.980730 + 0.195366i \(0.937410\pi\)
\(132\) 0 0
\(133\) 2.00000 + 2.00000i 0.173422 + 0.173422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.70820 6.70820i −0.573121 0.573121i 0.359879 0.932999i \(-0.382818\pi\)
−0.932999 + 0.359879i \(0.882818\pi\)
\(138\) 0 0
\(139\) 14.0000i 1.18746i −0.804663 0.593732i \(-0.797654\pi\)
0.804663 0.593732i \(-0.202346\pi\)
\(140\) 0 0
\(141\) 15.0000 + 6.70820i 1.26323 + 0.564933i
\(142\) 0 0
\(143\) −13.4164 + 13.4164i −1.12194 + 1.12194i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.09017 8.09017i −0.254873 0.667266i
\(148\) 0 0
\(149\) 13.4164 1.09911 0.549557 0.835456i \(-0.314796\pi\)
0.549557 + 0.835456i \(0.314796\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 9.47214 + 0.527864i 0.765777 + 0.0426753i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.00000 + 9.00000i −0.718278 + 0.718278i −0.968252 0.249974i \(-0.919578\pi\)
0.249974 + 0.968252i \(0.419578\pi\)
\(158\) 0 0
\(159\) −2.23607 + 5.00000i −0.177332 + 0.396526i
\(160\) 0 0
\(161\) 4.47214i 0.352454i
\(162\) 0 0
\(163\) −17.0000 17.0000i −1.33154 1.33154i −0.903991 0.427552i \(-0.859376\pi\)
−0.427552 0.903991i \(-0.640624\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.1803 + 11.1803i 0.865161 + 0.865161i 0.991932 0.126771i \(-0.0404614\pi\)
−0.126771 + 0.991932i \(0.540461\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 4.00000 + 4.47214i 0.305888 + 0.341993i
\(172\) 0 0
\(173\) −15.6525 + 15.6525i −1.19004 + 1.19004i −0.212979 + 0.977057i \(0.568317\pi\)
−0.977057 + 0.212979i \(0.931683\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 14.4721 5.52786i 1.08779 0.415500i
\(178\) 0 0
\(179\) 8.94427 0.668526 0.334263 0.942480i \(-0.391513\pi\)
0.334263 + 0.942480i \(0.391513\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 9.70820 3.70820i 0.717651 0.274118i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −10.0000 + 10.0000i −0.731272 + 0.731272i
\(188\) 0 0
\(189\) 2.23607 + 7.00000i 0.162650 + 0.509175i
\(190\) 0 0
\(191\) 4.47214i 0.323592i −0.986824 0.161796i \(-0.948271\pi\)
0.986824 0.161796i \(-0.0517287\pi\)
\(192\) 0 0
\(193\) 3.00000 + 3.00000i 0.215945 + 0.215945i 0.806787 0.590842i \(-0.201204\pi\)
−0.590842 + 0.806787i \(0.701204\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.70820 6.70820i −0.477940 0.477940i 0.426532 0.904472i \(-0.359735\pi\)
−0.904472 + 0.426532i \(0.859735\pi\)
\(198\) 0 0
\(199\) 18.0000i 1.27599i −0.770042 0.637993i \(-0.779765\pi\)
0.770042 0.637993i \(-0.220235\pi\)
\(200\) 0 0
\(201\) −1.00000 + 2.23607i −0.0705346 + 0.157720i
\(202\) 0 0
\(203\) 4.47214 4.47214i 0.313882 0.313882i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.527864 + 9.47214i −0.0366891 + 0.658359i
\(208\) 0 0
\(209\) −8.94427 −0.618688
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) 2.76393 + 7.23607i 0.189382 + 0.495807i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.00000 4.00000i 0.271538 0.271538i
\(218\) 0 0
\(219\) 2.23607 + 1.00000i 0.151099 + 0.0675737i
\(220\) 0 0
\(221\) 13.4164i 0.902485i
\(222\) 0 0
\(223\) 3.00000 + 3.00000i 0.200895 + 0.200895i 0.800383 0.599489i \(-0.204629\pi\)
−0.599489 + 0.800383i \(0.704629\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.1803 + 11.1803i 0.742065 + 0.742065i 0.972975 0.230910i \(-0.0741703\pi\)
−0.230910 + 0.972975i \(0.574170\pi\)
\(228\) 0 0
\(229\) 12.0000i 0.792982i 0.918039 + 0.396491i \(0.129772\pi\)
−0.918039 + 0.396491i \(0.870228\pi\)
\(230\) 0 0
\(231\) −10.0000 4.47214i −0.657952 0.294245i
\(232\) 0 0
\(233\) 20.1246 20.1246i 1.31841 1.31841i 0.403370 0.915037i \(-0.367839\pi\)
0.915037 0.403370i \(-0.132161\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −3.70820 9.70820i −0.240874 0.630616i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 0 0
\(243\) 3.90983 + 15.0902i 0.250816 + 0.968035i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 + 6.00000i −0.381771 + 0.381771i
\(248\) 0 0
\(249\) −6.70820 + 15.0000i −0.425115 + 0.950586i
\(250\) 0 0
\(251\) 13.4164i 0.846836i −0.905934 0.423418i \(-0.860830\pi\)
0.905934 0.423418i \(-0.139170\pi\)
\(252\) 0 0
\(253\) −10.0000 10.0000i −0.628695 0.628695i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.6525 15.6525i −0.976375 0.976375i 0.0233527 0.999727i \(-0.492566\pi\)
−0.999727 + 0.0233527i \(0.992566\pi\)
\(258\) 0 0
\(259\) 6.00000i 0.372822i
\(260\) 0 0
\(261\) 10.0000 8.94427i 0.618984 0.553637i
\(262\) 0 0
\(263\) 15.6525 15.6525i 0.965173 0.965173i −0.0342406 0.999414i \(-0.510901\pi\)
0.999414 + 0.0342406i \(0.0109013\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.23607 2.76393i 0.442840 0.169150i
\(268\) 0 0
\(269\) −22.3607 −1.36335 −0.681677 0.731653i \(-0.738749\pi\)
−0.681677 + 0.731653i \(0.738749\pi\)
\(270\) 0 0
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 0 0
\(273\) −9.70820 + 3.70820i −0.587567 + 0.224431i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.00000 + 9.00000i −0.540758 + 0.540758i −0.923751 0.382993i \(-0.874893\pi\)
0.382993 + 0.923751i \(0.374893\pi\)
\(278\) 0 0
\(279\) 8.94427 8.00000i 0.535480 0.478947i
\(280\) 0 0
\(281\) 26.8328i 1.60071i −0.599525 0.800356i \(-0.704644\pi\)
0.599525 0.800356i \(-0.295356\pi\)
\(282\) 0 0
\(283\) −17.0000 17.0000i −1.01055 1.01055i −0.999944 0.0106013i \(-0.996625\pi\)
−0.0106013 0.999944i \(-0.503375\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.94427 8.94427i −0.527964 0.527964i
\(288\) 0 0
\(289\) 7.00000i 0.411765i
\(290\) 0 0
\(291\) 9.00000 20.1246i 0.527589 1.17973i
\(292\) 0 0
\(293\) −6.70820 + 6.70820i −0.391897 + 0.391897i −0.875363 0.483466i \(-0.839378\pi\)
0.483466 + 0.875363i \(0.339378\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −20.6525 10.6525i −1.19838 0.618119i
\(298\) 0 0
\(299\) −13.4164 −0.775891
\(300\) 0 0
\(301\) 6.00000 0.345834
\(302\) 0 0
\(303\) −5.52786 14.4721i −0.317567 0.831402i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 21.0000 21.0000i 1.19853 1.19853i 0.223928 0.974606i \(-0.428112\pi\)
0.974606 0.223928i \(-0.0718879\pi\)
\(308\) 0 0
\(309\) 2.23607 + 1.00000i 0.127205 + 0.0568880i
\(310\) 0 0
\(311\) 4.47214i 0.253592i −0.991929 0.126796i \(-0.959531\pi\)
0.991929 0.126796i \(-0.0404693\pi\)
\(312\) 0 0
\(313\) 3.00000 + 3.00000i 0.169570 + 0.169570i 0.786790 0.617220i \(-0.211741\pi\)
−0.617220 + 0.786790i \(0.711741\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.1246 + 20.1246i 1.13031 + 1.13031i 0.990125 + 0.140186i \(0.0447699\pi\)
0.140186 + 0.990125i \(0.455230\pi\)
\(318\) 0 0
\(319\) 20.0000i 1.11979i
\(320\) 0 0
\(321\) −5.00000 2.23607i −0.279073 0.124805i
\(322\) 0 0
\(323\) −4.47214 + 4.47214i −0.248836 + 0.248836i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.94427 + 12.9443i 0.273419 + 0.715820i
\(328\) 0 0
\(329\) −13.4164 −0.739671
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 0.708204 12.7082i 0.0388093 0.696405i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9.00000 + 9.00000i −0.490261 + 0.490261i −0.908388 0.418127i \(-0.862687\pi\)
0.418127 + 0.908388i \(0.362687\pi\)
\(338\) 0 0
\(339\) −2.23607 + 5.00000i −0.121447 + 0.271563i
\(340\) 0 0
\(341\) 17.8885i 0.968719i
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.5967 24.5967i −1.32042 1.32042i −0.913433 0.406990i \(-0.866578\pi\)
−0.406990 0.913433i \(-0.633422\pi\)
\(348\) 0 0
\(349\) 4.00000i 0.214115i −0.994253 0.107058i \(-0.965857\pi\)
0.994253 0.107058i \(-0.0341429\pi\)
\(350\) 0 0
\(351\) −21.0000 + 6.70820i −1.12090 + 0.358057i
\(352\) 0 0
\(353\) −6.70820 + 6.70820i −0.357042 + 0.357042i −0.862721 0.505680i \(-0.831242\pi\)
0.505680 + 0.862721i \(0.331242\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.23607 + 2.76393i −0.382973 + 0.146283i
\(358\) 0 0
\(359\) 35.7771 1.88824 0.944121 0.329598i \(-0.106913\pi\)
0.944121 + 0.329598i \(0.106913\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 0 0
\(363\) 14.5623 5.56231i 0.764323 0.291945i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.00000 1.00000i 0.0521996 0.0521996i −0.680525 0.732725i \(-0.738248\pi\)
0.732725 + 0.680525i \(0.238248\pi\)
\(368\) 0 0
\(369\) −17.8885 20.0000i −0.931240 1.04116i
\(370\) 0 0
\(371\) 4.47214i 0.232182i
\(372\) 0 0
\(373\) 23.0000 + 23.0000i 1.19089 + 1.19089i 0.976816 + 0.214078i \(0.0686748\pi\)
0.214078 + 0.976816i \(0.431325\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 13.4164 + 13.4164i 0.690980 + 0.690980i
\(378\) 0 0
\(379\) 2.00000i 0.102733i 0.998680 + 0.0513665i \(0.0163577\pi\)
−0.998680 + 0.0513665i \(0.983642\pi\)
\(380\) 0 0
\(381\) −13.0000 + 29.0689i −0.666010 + 1.48924i
\(382\) 0 0
\(383\) 6.70820 6.70820i 0.342773 0.342773i −0.514636 0.857409i \(-0.672073\pi\)
0.857409 + 0.514636i \(0.172073\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.7082 + 0.708204i 0.645994 + 0.0360000i
\(388\) 0 0
\(389\) 13.4164 0.680239 0.340119 0.940382i \(-0.389532\pi\)
0.340119 + 0.940382i \(0.389532\pi\)
\(390\) 0 0
\(391\) −10.0000 −0.505722
\(392\) 0 0
\(393\) −2.76393 7.23607i −0.139422 0.365011i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 11.0000 11.0000i 0.552074 0.552074i −0.374965 0.927039i \(-0.622345\pi\)
0.927039 + 0.374965i \(0.122345\pi\)
\(398\) 0 0
\(399\) −4.47214 2.00000i −0.223887 0.100125i
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 12.0000 + 12.0000i 0.597763 + 0.597763i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 13.4164 + 13.4164i 0.665027 + 0.665027i
\(408\) 0 0
\(409\) 12.0000i 0.593362i 0.954977 + 0.296681i \(0.0958798\pi\)
−0.954977 + 0.296681i \(0.904120\pi\)
\(410\) 0 0
\(411\) 15.0000 + 6.70820i 0.739895 + 0.330891i
\(412\) 0 0
\(413\) −8.94427 + 8.94427i −0.440119 + 0.440119i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.65248 + 22.6525i 0.423714 + 1.10930i
\(418\) 0 0
\(419\) 26.8328 1.31087 0.655434 0.755252i \(-0.272486\pi\)
0.655434 + 0.755252i \(0.272486\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) −28.4164 1.58359i −1.38165 0.0769969i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.00000 + 6.00000i −0.290360 + 0.290360i
\(428\) 0 0
\(429\) 13.4164 30.0000i 0.647750 1.44841i
\(430\) 0 0
\(431\) 31.3050i 1.50791i 0.656928 + 0.753953i \(0.271855\pi\)
−0.656928 + 0.753953i \(0.728145\pi\)
\(432\) 0 0
\(433\) −17.0000 17.0000i −0.816968 0.816968i 0.168700 0.985668i \(-0.446043\pi\)
−0.985668 + 0.168700i \(0.946043\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.47214 4.47214i −0.213931 0.213931i
\(438\) 0 0
\(439\) 22.0000i 1.05000i 0.851101 + 0.525001i \(0.175935\pi\)
−0.851101 + 0.525001i \(0.824065\pi\)
\(440\) 0 0
\(441\) 10.0000 + 11.1803i 0.476190 + 0.532397i
\(442\) 0 0
\(443\) −20.1246 + 20.1246i −0.956149 + 0.956149i −0.999078 0.0429290i \(-0.986331\pi\)
0.0429290 + 0.999078i \(0.486331\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −21.7082 + 8.29180i −1.02676 + 0.392188i
\(448\) 0 0
\(449\) 4.47214 0.211053 0.105527 0.994416i \(-0.466347\pi\)
0.105527 + 0.994416i \(0.466347\pi\)
\(450\) 0 0
\(451\) 40.0000 1.88353
\(452\) 0 0
\(453\) −6.47214 + 2.47214i −0.304087 + 0.116151i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.00000 3.00000i 0.140334 0.140334i −0.633450 0.773784i \(-0.718362\pi\)
0.773784 + 0.633450i \(0.218362\pi\)
\(458\) 0 0
\(459\) −15.6525 + 5.00000i −0.730595 + 0.233380i
\(460\) 0 0
\(461\) 8.94427i 0.416576i −0.978068 0.208288i \(-0.933211\pi\)
0.978068 0.208288i \(-0.0667892\pi\)
\(462\) 0 0
\(463\) 19.0000 + 19.0000i 0.883005 + 0.883005i 0.993839 0.110834i \(-0.0353522\pi\)
−0.110834 + 0.993839i \(0.535352\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.23607 + 2.23607i 0.103473 + 0.103473i 0.756948 0.653475i \(-0.226690\pi\)
−0.653475 + 0.756948i \(0.726690\pi\)
\(468\) 0 0
\(469\) 2.00000i 0.0923514i
\(470\) 0 0
\(471\) 9.00000 20.1246i 0.414698 0.927293i
\(472\) 0 0
\(473\) −13.4164 + 13.4164i −0.616887 + 0.616887i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.527864 9.47214i 0.0241692 0.433699i
\(478\) 0 0
\(479\) −35.7771 −1.63470 −0.817348 0.576144i \(-0.804557\pi\)
−0.817348 + 0.576144i \(0.804557\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) −2.76393 7.23607i −0.125763 0.329252i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 21.0000 21.0000i 0.951601 0.951601i −0.0472808 0.998882i \(-0.515056\pi\)
0.998882 + 0.0472808i \(0.0150556\pi\)
\(488\) 0 0
\(489\) 38.0132 + 17.0000i 1.71901 + 0.768767i
\(490\) 0 0
\(491\) 22.3607i 1.00912i 0.863376 + 0.504562i \(0.168346\pi\)
−0.863376 + 0.504562i \(0.831654\pi\)
\(492\) 0 0
\(493\) 10.0000 + 10.0000i 0.450377 + 0.450377i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.47214 4.47214i −0.200603 0.200603i
\(498\) 0 0
\(499\) 38.0000i 1.70111i −0.525883 0.850557i \(-0.676265\pi\)
0.525883 0.850557i \(-0.323735\pi\)
\(500\) 0 0
\(501\) −25.0000 11.1803i −1.11692 0.499501i
\(502\) 0 0
\(503\) 6.70820 6.70820i 0.299104 0.299104i −0.541559 0.840663i \(-0.682166\pi\)
0.840663 + 0.541559i \(0.182166\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.09017 8.09017i −0.137239 0.359297i
\(508\) 0 0
\(509\) 4.47214 0.198224 0.0991120 0.995076i \(-0.468400\pi\)
0.0991120 + 0.995076i \(0.468400\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 0 0
\(513\) −9.23607 4.76393i −0.407782 0.210333i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 30.0000 30.0000i 1.31940 1.31940i
\(518\) 0 0
\(519\) 15.6525 35.0000i 0.687067 1.53633i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 3.00000 + 3.00000i 0.131181 + 0.131181i 0.769649 0.638468i \(-0.220431\pi\)
−0.638468 + 0.769649i \(0.720431\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.94427 + 8.94427i 0.389619 + 0.389619i
\(528\) 0 0
\(529\) 13.0000i 0.565217i
\(530\) 0 0
\(531\) −20.0000 + 17.8885i −0.867926 + 0.776297i
\(532\) 0 0
\(533\) 26.8328 26.8328i 1.16226 1.16226i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −14.4721 + 5.52786i −0.624519 + 0.238545i
\(538\) 0 0
\(539\) −22.3607 −0.963143
\(540\) 0 0
\(541\) −26.0000 −1.11783 −0.558914 0.829226i \(-0.688782\pi\)
−0.558914 + 0.829226i \(0.688782\pi\)
\(542\) 0 0
\(543\) −22.6525 + 8.65248i −0.972111 + 0.371313i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −27.0000 + 27.0000i −1.15444 + 1.15444i −0.168783 + 0.985653i \(0.553984\pi\)
−0.985653 + 0.168783i \(0.946016\pi\)
\(548\) 0 0
\(549\) −13.4164 + 12.0000i −0.572598 + 0.512148i
\(550\) 0 0
\(551\) 8.94427i 0.381039i
\(552\) 0 0
\(553\) 6.00000 + 6.00000i 0.255146 + 0.255146i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.70820 6.70820i −0.284236 0.284236i 0.550560 0.834796i \(-0.314414\pi\)
−0.834796 + 0.550560i \(0.814414\pi\)
\(558\) 0 0
\(559\) 18.0000i 0.761319i
\(560\) 0 0
\(561\) 10.0000 22.3607i 0.422200 0.944069i
\(562\) 0 0
\(563\) 6.70820 6.70820i 0.282717 0.282717i −0.551475 0.834192i \(-0.685935\pi\)
0.834192 + 0.551475i \(0.185935\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −7.94427 9.94427i −0.333628 0.417620i
\(568\) 0 0
\(569\) 22.3607 0.937408 0.468704 0.883355i \(-0.344721\pi\)
0.468704 + 0.883355i \(0.344721\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 0 0
\(573\) 2.76393 + 7.23607i 0.115465 + 0.302291i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000 11.0000i 0.457936 0.457936i −0.440041 0.897977i \(-0.645036\pi\)
0.897977 + 0.440041i \(0.145036\pi\)
\(578\) 0 0
\(579\) −6.70820 3.00000i −0.278783 0.124676i
\(580\) 0 0
\(581\) 13.4164i 0.556606i
\(582\) 0 0
\(583\) 10.0000 + 10.0000i 0.414158 + 0.414158i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.70820 6.70820i −0.276877 0.276877i 0.554984 0.831861i \(-0.312724\pi\)
−0.831861 + 0.554984i \(0.812724\pi\)
\(588\) 0 0
\(589\) 8.00000i 0.329634i
\(590\) 0 0
\(591\) 15.0000 + 6.70820i 0.617018 + 0.275939i
\(592\) 0 0
\(593\) 11.1803 11.1803i 0.459122 0.459122i −0.439246 0.898367i \(-0.644754\pi\)
0.898367 + 0.439246i \(0.144754\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 11.1246 + 29.1246i 0.455300 + 1.19199i
\(598\) 0 0
\(599\) −35.7771 −1.46181 −0.730906 0.682478i \(-0.760902\pi\)
−0.730906 + 0.682478i \(0.760902\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0.236068 4.23607i 0.00961343 0.172506i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −27.0000 + 27.0000i −1.09590 + 1.09590i −0.101011 + 0.994885i \(0.532208\pi\)
−0.994885 + 0.101011i \(0.967792\pi\)
\(608\) 0 0
\(609\) −4.47214 + 10.0000i −0.181220 + 0.405220i
\(610\) 0 0
\(611\) 40.2492i 1.62831i
\(612\) 0 0
\(613\) −21.0000 21.0000i −0.848182 0.848182i 0.141724 0.989906i \(-0.454735\pi\)
−0.989906 + 0.141724i \(0.954735\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.1246 + 20.1246i 0.810186 + 0.810186i 0.984662 0.174475i \(-0.0558229\pi\)
−0.174475 + 0.984662i \(0.555823\pi\)
\(618\) 0 0
\(619\) 42.0000i 1.68812i 0.536247 + 0.844061i \(0.319842\pi\)
−0.536247 + 0.844061i \(0.680158\pi\)
\(620\) 0 0
\(621\) −5.00000 15.6525i −0.200643 0.628112i
\(622\) 0 0
\(623\) −4.47214 + 4.47214i −0.179172 + 0.179172i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 14.4721 5.52786i 0.577961 0.220762i
\(628\) 0 0
\(629\) 13.4164 0.534947
\(630\) 0 0
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 0 0
\(633\) 25.8885 9.88854i 1.02898 0.393034i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −15.0000 + 15.0000i −0.594322 + 0.594322i
\(638\) 0 0
\(639\) −8.94427 10.0000i −0.353830 0.395594i
\(640\) 0 0
\(641\) 8.94427i 0.353278i 0.984276 + 0.176639i \(0.0565224\pi\)
−0.984276 + 0.176639i \(0.943478\pi\)
\(642\) 0 0
\(643\) −21.0000 21.0000i −0.828159 0.828159i 0.159103 0.987262i \(-0.449140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.6525 15.6525i −0.615362 0.615362i 0.328976 0.944338i \(-0.393296\pi\)
−0.944338 + 0.328976i \(0.893296\pi\)
\(648\) 0 0
\(649\) 40.0000i 1.57014i
\(650\) 0 0
\(651\) −4.00000 + 8.94427i −0.156772 + 0.350554i
\(652\) 0 0
\(653\) 20.1246 20.1246i 0.787537 0.787537i −0.193553 0.981090i \(-0.562001\pi\)
0.981090 + 0.193553i \(0.0620011\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −4.23607 0.236068i −0.165265 0.00920989i
\(658\) 0 0
\(659\) 8.94427 0.348419 0.174210 0.984709i \(-0.444263\pi\)
0.174210 + 0.984709i \(0.444263\pi\)
\(660\) 0 0
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 0 0
\(663\) −8.29180 21.7082i −0.322027 0.843077i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −10.0000 + 10.0000i −0.387202 + 0.387202i
\(668\) 0 0
\(669\) −6.70820 3.00000i −0.259354 0.115987i
\(670\) 0 0
\(671\) 26.8328i 1.03587i
\(672\) 0 0
\(673\) −1.00000 1.00000i −0.0385472 0.0385472i 0.687570 0.726118i \(-0.258677\pi\)
−0.726118 + 0.687570i \(0.758677\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −24.5967 24.5967i −0.945330 0.945330i 0.0532513 0.998581i \(-0.483042\pi\)
−0.998581 + 0.0532513i \(0.983042\pi\)
\(678\) 0 0
\(679\) 18.0000i 0.690777i
\(680\) 0 0
\(681\) −25.0000 11.1803i −0.958002 0.428432i
\(682\) 0 0
\(683\) −20.1246 + 20.1246i −0.770047 + 0.770047i −0.978114 0.208068i \(-0.933283\pi\)
0.208068 + 0.978114i \(0.433283\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −7.41641 19.4164i −0.282954 0.740782i
\(688\) 0 0
\(689\) 13.4164 0.511124
\(690\) 0 0
\(691\) −48.0000 −1.82601 −0.913003 0.407953i \(-0.866243\pi\)
−0.913003 + 0.407953i \(0.866243\pi\)
\(692\) 0 0
\(693\) 18.9443 + 1.05573i 0.719633 + 0.0401038i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 20.0000 20.0000i 0.757554 0.757554i
\(698\) 0 0
\(699\) −20.1246 + 45.0000i −0.761183 + 1.70206i
\(700\) 0 0
\(701\) 35.7771i 1.35128i −0.737231 0.675641i \(-0.763867\pi\)
0.737231 0.675641i \(-0.236133\pi\)
\(702\) 0 0
\(703\) 6.00000 + 6.00000i 0.226294 + 0.226294i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.94427 + 8.94427i 0.336384 + 0.336384i
\(708\) 0 0
\(709\) 28.0000i 1.05156i −0.850620 0.525781i \(-0.823773\pi\)
0.850620 0.525781i \(-0.176227\pi\)
\(710\) 0 0
\(711\) 12.0000 + 13.4164i 0.450035 + 0.503155i
\(712\) 0 0
\(713\) −8.94427 + 8.94427i −0.334966 + 0.334966i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −35.7771 −1.33426 −0.667130 0.744941i \(-0.732478\pi\)
−0.667130 + 0.744941i \(0.732478\pi\)
\(720\) 0 0
\(721\) −2.00000 −0.0744839
\(722\) 0 0
\(723\) 42.0689 16.0689i 1.56456 0.597608i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 21.0000 21.0000i 0.778847 0.778847i −0.200788 0.979635i \(-0.564350\pi\)
0.979635 + 0.200788i \(0.0643502\pi\)
\(728\) 0 0
\(729\) −15.6525 22.0000i −0.579721 0.814815i
\(730\) 0 0
\(731\) 13.4164i 0.496224i
\(732\) 0 0
\(733\) −1.00000 1.00000i −0.0369358 0.0369358i 0.688398 0.725333i \(-0.258314\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.47214 + 4.47214i 0.164733 + 0.164733i
\(738\) 0 0
\(739\) 14.0000i 0.514998i −0.966279 0.257499i \(-0.917102\pi\)
0.966279 0.257499i \(-0.0828985\pi\)
\(740\) 0 0
\(741\) 6.00000 13.4164i 0.220416 0.492864i
\(742\) 0 0
\(743\) −11.1803 + 11.1803i −0.410167 + 0.410167i −0.881797 0.471630i \(-0.843666\pi\)
0.471630 + 0.881797i \(0.343666\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.58359 28.4164i 0.0579406 1.03970i
\(748\) 0 0
\(749\) 4.47214 0.163408
\(750\) 0 0
\(751\) 12.0000 0.437886 0.218943 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) 0 0
\(753\) 8.29180 + 21.7082i 0.302170 + 0.791091i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −9.00000 + 9.00000i −0.327111 + 0.327111i −0.851487 0.524376i \(-0.824299\pi\)
0.524376 + 0.851487i \(0.324299\pi\)
\(758\) 0 0
\(759\) 22.3607 + 10.0000i 0.811641 + 0.362977i
\(760\) 0 0
\(761\) 17.8885i 0.648459i 0.945978 + 0.324230i \(0.105105\pi\)
−0.945978 + 0.324230i \(0.894895\pi\)
\(762\) 0 0
\(763\) −8.00000 8.00000i −0.289619 0.289619i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −26.8328 26.8328i −0.968877 0.968877i
\(768\) 0 0
\(769\) 8.00000i 0.288487i −0.989542 0.144244i \(-0.953925\pi\)
0.989542 0.144244i \(-0.0460749\pi\)
\(770\) 0 0
\(771\) 35.0000 + 15.6525i 1.26049 + 0.563710i
\(772\) 0 0
\(773\) −6.70820 + 6.70820i −0.241277 + 0.241277i −0.817378 0.576101i \(-0.804573\pi\)
0.576101 + 0.817378i \(0.304573\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3.70820 + 9.70820i 0.133031 + 0.348280i
\(778\) 0 0
\(779\) 17.8885 0.640924
\(780\) 0 0
\(781\) 20.0000 0.715656
\(782\) 0 0
\(783\) −10.6525 + 20.6525i −0.380688 + 0.738059i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −19.0000 + 19.0000i −0.677277 + 0.677277i −0.959383 0.282106i \(-0.908967\pi\)
0.282106 + 0.959383i \(0.408967\pi\)
\(788\) 0 0
\(789\) −15.6525 + 35.0000i −0.557243 + 1.24603i
\(790\) 0 0
\(791\) 4.47214i 0.159011i
\(792\) 0 0
\(793\) −18.0000 18.0000i −0.639199 0.639199i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.1246 + 20.1246i 0.712850 + 0.712850i 0.967131 0.254280i \(-0.0818386\pi\)
−0.254280 + 0.967131i \(0.581839\pi\)
\(798\) 0 0
\(799\) 30.0000i 1.06132i
\(800\) 0 0